Cure time adjustment for a rubber article

ABSTRACT

A method for curing a rubber article including maintaining a measured curing temperature between a high temperature limit (TH) and a low temperature limit (TL). The TH TL are derived from high and low temperature curing curves respectively. Other steps may include obtaining a curing target A1 or A2, wherein A1 and A2 are areas between the high temperature curing curve and a base temperature (TB) and the low temperature curing curve respectively wherein TB is selected to make A1 and A2 within at least 10% of each other and determining an area under a measured curing curve, the area under the measured curing curve being between the measured curing curve and the TB, wherein the measured curing curve is defined as a plot of the measured curing temperature over time.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to rubber curing and more specifically,to curing of rubber articles.

2. Description of the Related Art

When tires become worn, they can be restored with new tread. Large trucktires and bus tires, for example, are typically retreaded as part of aroutine tire-management program. The carcass of a these types of tiresis expected to last several hundred thousand miles and be amenable tohaving a new tread adhered to it several times. Such tires are quiteexpensive and are therefore bought with the expectation that their highinitial costs are offset by the long service life of the carcass and thelow comparative cost of retreading. Indeed, the economics included inthe selection and purchase of such tires often dictate that the originaltires be capable of being retreaded as many as three or four times.

A variety of procedures and different types of equipment are availablefor use in recapping or retreading pneumatic tires. One of the firststeps in retreading a worn tire is to remove remaining tread materialfrom the tire carcass, for example, by a procedure known as buffing.Next a layer of green (uncured) rubber, known as “cushion gum,” may beapplied to the carcass. This layer of extruded uncured rubber may bestitched or adhesively bonded to the carcass. Next, a tread band isapplied atop the layer of cushion gum. In the cold recapping process,the tread is cured rubber, and has a tread pattern already impressed inits outer surface. The tire is then placed in an autoclave, and heatedunder pressure for an appropriate time to induce curing of the gumlayer, and bonding of the gum layer to the tread and the carcass. In thehot recapping process, the tread is uncured rubber, and has no treadpattern. The tire is then placed in a tire mold and heated underpressure for an appropriate time to cure the gum layer and the tread,and to cause the gum layer to bind with the tread and the carcass. Theterm “cure” refers to the formation of cross-links between the elastomermolecules in the rubber compound, otherwise known as vulcanization.

SUMMARY OF THE INVENTION

Particular embodiments of the present invention include methods,computer program products and a system for curing a rubber article.Methods that are particular embodiments of the present invention includethe step of maintaining a measured curing temperature (TM) between ahigh temperature limit (TH) and a low temperature limit (TL), whereinthe TH is derived from a high temperature curing curve and the TL isderived from a low temperature curing curve. Other steps may includeobtaining a curing target A1 or A2, wherein A1 is an area between thehigh temperature curing curve and a base temperature (TB) and A2 is anarea between the low temperature curing curve and the TB, wherein the TBis selected to make A1 and A2 within at least 10% of each other anddetermining an area under a measured curing curve, the area under themeasured curing curve being between the measured curing curve and theTB, wherein the measured curing curve is defined as a plot of themeasured curing temperature over time.

Particular embodiments of such methods may further include the steps ofindicating a completed cure when the area under the measured curingcurve reaches the curing target and obtaining the base temperature.

Particular embodiments of such methods may further include the step ofindicating a completed cure when the area under the measured curingcurve reaches the curing target.

Particular embodiments of the present invention further include acomputer program product including instructions embodied on a computerreadable storage medium, the computer program product acting to cure arubber article. Particular embodiments of the present invention, thatare instructions embodied on a computer readable storage medium forcuring a rubber article, include instructions for performing the methodsdescribed above.

Particular embodiments of the present invention further include a systemfor curing a rubber article. The system includes an autoclave comprisinga chamber that is controllably heated for curing the rubber article anda temperature sensor for generating a signal as a function of a curingtemperature in the chamber of the autoclave. The system further includesa controller for controlling the curing temperature in the autoclave,the controller comprising a processor and a memory storage device thatstores instructions executable by the processor. These executableinstructions include the instructions to implement the methods disclosedabove.

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more detailed descriptionsof particular embodiments of the invention, as illustrated in theaccompanying drawing wherein like reference numbers represent like partsof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic drawing of an autoclave suitable for curing aretread tire.

FIG. 2 is a schematic drawing of a controller suitable for controllingthe temperature in an autoclave in accordance with particularembodiments of the present invention.

FIG. 3 is a graph showing compliant curing curves at varyingtemperatures for a given rubber article.

FIG. 4 is a graph showing compliant curing curves at varyingtemperatures for a given rubber article.

FIG. 5 is a graph showing a typical cure cycle for a rubber article.

FIG. 6 is a graph showing the area between a high temperature curingcurve and the base temperature.

FIG. 7 is a graph showing the area between a low temperature curingcurve and the base temperature.

FIG. 8 is a graph showing the area between a measured curing curve andthe base temperature in accordance with particular embodiments of thepresent invention.

FIG. 9 is a flowchart of an exemplary method for curing a rubber aexecutable on the system of FIG. 1 in accordance with the presentinvention.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

The present invention provides methods, computer programs and systemsfor adjusting the cure time of a rubber article. Particular embodimentsof the present invention include a retread tire as the article.

Uncured rubber is easily deformed when warm and is quite brittle whencold. Curing a rubber article provides cross-links between the polymerchains of the rubber and imparts the property of elasticity that istypical of articles made of cured rubber. A rubber article may be curedin an autoclave by holding the article at a set temperature and at a setpressure for a set period of time. If the temperature fluctuates duringthe curing cycle by more than a few degrees of acceptable tolerance, thecure may be declared as a noncompliant cure and the improperly curedarticles may have to be discarded. Particular embodiments of the presentinvention provide methods for automatically adjusting the cure time toaccount for wider temperature fluctuations and still provide for acompliant cure.

An autoclave is commonly used in the industry for curing rubberarticles. The autoclave includes a chamber for containing the rubberarticles during the curing process and a mechanism for controlling thetemperature and pressure within the autoclave.

FIG. 1 is a schematic drawing of an autoclave 10 suitable for curing aretread tire. The autoclave 10 includes an elongated chamber 11 forcontaining the tires 12 during the curing process. A temperatureindicator 19, such as a thermocouple, sends a signal to the controller20. The controller 20 controls the temperature in the autoclave bysending a signal to a control device, such as a valve 17, which controlsthe heat input into the autoclave. The heat input may be provided, forexample, by an electric resistance coil, by a heating medium such assteam or by a circulating medium such as hot water, hot oil or so forth.In the embodiment shown, the heating medium is a circulating heatingmedium, such as hot water, that includes a hot water inlet 16 and a hotwater outlet 18 to and from the heat exchanger 13.

Air is circulated through the autoclave 10 by flowing through the heatexchanger 13 where the air is heated by the circulating heating medium.The air enters the heat exchanger at the air inlet 14 and exits the heatexchanger 13 at the air outlet 15, where it passes into the air supplyduct 27. The air supply duct 27 opens into the far end of the chamber 11and flows back to the air inlet 14 of the heat exchanger 13. Thecirculating air passes over the tires 12 to heat them during the curingprocess.

FIG. 2 is a schematic drawing of a controller suitable for controllingthe temperature in the autoclave of FIG. 1 in accordance with particularembodiments of the present invention. The controller 20 may be aprogrammable logic controller as shown in FIG. 2 or other device havinga processor that can execute programmed instructions, such as, forexample, a personal computer, main frame computer or other controlsystem.

The controller 20 interprets the signal received from the temperatureindicator 19. Without limitation, the signal from the temperatureindicator 19 may be sent by wireless communication to the controller 20,such as by infrared signal or by radio frequency, by one or more cables,including fiber optics, or by any other methods or devices known tothose having ordinary skill in the art.

The programmable logic controller 20 generally receives a signal fromthe temperature indicator 19 to monitor and control the temperature inthe autoclave 10. The controller 20 provides a signal 26 to the valve 17to manipulate the valve 17 and thereby control the temperature in thechamber 11.

The controller 20 includes a processor 21, which may be amicroprocessor. The controller 20 further includes a memory storagedevice 22, such as RAM (random access memory), ROM (read-only memory),PROM (programmable read-only memory) and at least one input/output (I/O)cable 26 for communicating with the temperature indicator 19 and thevalve 17. Further, the controller 20 may include an I/O slot 23 forhousing an I/O card having I/O cable connector 29. An operator mayutilize a user interface 28 to monitor the temperature measurements andto program, or otherwise control or instruct, the operation ofcontroller 20 and the autoclave 10, which includes performing each stepand method associated with curing a rubber article in accordance toparticular embodiments of the present invention.

Generally, the controller 20 may be programmed by any known graphical ortext language. Programmed instructions, data, input and output may bestored in a memory storage device 22, which is accessible to theprocessor 21. Particularly, programmed instructions related to themethods disclosed herein may be stored in the memory storage device 22and executed by the processor 21. The memory device 22 may comprise anycommercially known storage device, such as hard disk drives, opticalstorage devices, flash memory, and the like. The processor 21 executesprogrammed instructions pertaining to the methods disclosed herein aswell as other operations discussed herein. The memory storage device 22also stores inputs, outputs, and other information, such as, forexample, temperatures measured within the autoclave 10 over the curingtime period, base temperatures input by an operator and/or curingtargets as described below.

A rubber article may include, for example, hoses, belts, vibrationmounts, bumpers, tires and parts of tires including cushion gums, andrepairs using the methods and systems disclosed herein.

During the curing of a rubber article, a sufficient amount of heatenergy is provided to the rubber article to complete the cure of therubber article. Such methods are well known in the industry and resultin a curing process tailored for the articles being cured. The curingprocess, as noted above, includes setting a time period for which thearticles to be cured are maintained at a set temperature and a setpressure. The required time period and temperature over which thearticles must be held to achieve a compliant cure may be described by acuring curve, which plots the curing temperature over time.

The curing curves are typically derived through experimentation orfinite analysis methods. ASTM D2084 and ISO 3417 describe how to measurecure times required for rubber compounds using an oscillating rheometer.Factors that are included in determining the curing process and thecuring curves include, for example, the rubber composition and thethickness of the rubber article. As known by one having ordinary skillin the art, a rubber article must be cured for a sufficient time thatthe temperature of the rubber article is increased to the desiredtemperature to complete a compliant cure.

For example, a particular rubber article may be cured at a highertemperature for a shorter period of time or at a lower temperature for alonger period of time to achieve a compliant cure of the article.Likewise, the temperature profile that is held for the cure time, and isillustrated by a curing curve, does not have to be constant. Theseconcepts are illustrated in FIGS. 3 and 4.

FIG. 3 is a graph showing compliant curing curves at varioustemperatures for a given rubber article. As shown, a compliant cure ofthe rubber article may be achieved by maintaining the temperature alongthe curing curve 51 at the highest temperature for the shortest periodof time. Alternatively, the article may be cured along the intermediatetemperature curing curve 52 for a longer period of time to achieve acompliant cure. Further, as another alternative, the article may becured along the lowest temperature curing curve 53 for an even longerperiod of time to achieve a compliant cure. Each of these curing curves51, 52, 53 are obtained by methods well known by those having ordinaryskill in the art.

FIG. 4 is a graph showing compliant curing curves at varyingtemperatures for a given rubber article. The graphs shown in FIG. 4demonstrate that the temperatures do not have to follow a linearrelationship, as those shown in FIG. 3, to obtain a compliant cure. Asin FIG. 4, the higher temperature curing curve 61 provides a compliantcure over a shorter period of time than the lower temperature curingcurve 62.

FIG. 5 is a graph showing a typical cure cycle for a rubber article. Thegraph shows the measured temperature in an autoclave over a period oftime during which the article is being cured. The measured temperatureis shown increasing from ambient to the narrow curing temperature rangeTC. For a compliant curve, the temperature will be held within thetemperature range TC. The narrow curing temperature range TC isdetermined to be the acceptable tolerance around a curing curve, such asthose shown in FIGS. 3 and 4. This tolerance is typically no more thanabout plus or minus 5° C.

After the measured temperature reaches the curing temperature range TC,the cure time is started at “ts” and continues for the prescribed setperiod of time ending at “tf.” The cure is considered compliant as longas the temperature in the autoclave stays within the acceptabletolerance of the narrow curing temperature range TC over the prescribedperiod of time from “ts” to “tf.”

As noted previously, a problem in the industry is that if thetemperature in the autoclave is not maintained along the prescribedcuring curve, e.g., TC in FIG. 5, and the temperature drops below theprescribed curing temperature range, then the cure of the rubberarticles is non-compliant and the articles may have to be scrapped orreconditioned, increasing the time and cost for the process. Particularembodiments of the present invention include, inter alia, methods foradjusting a cure time for a rubber article to prevent or minimize theoccurrence of such a non-compliant cure and the associated costs.

In one embodiment of the present invention, a method for curing a rubberarticle includes the step of maintaining a measured curing temperature(TM) that is between a high temperature limit (TH) and a low temperaturelimit (TL). The high temperature limit and the low temperature limit areeach derived from a high temperature curing curve and a low temperaturecuring curve respectively. These different curing curves each provide acompliant cure for the rubber article, one at a higher temperature for ashorter period of time and one at a lower temperature for a longerperiod of time.

For example, as shown in FIG. 3, the curing curve 51 shown at thehighest temperature may be considered a high temperature curing curseand the curing curve 53 shown at the lowest temperature may beconsidered a low temperature curing curve. The third curve 52 shown maybe considered either a high temperature curing curve when paired withthe low temperature curing curve 53 or it 52 may be considered a lowtemperature curing curve when paired with the high temperature curingcurve 51.

In particular embodiments of the present invention, the high temperaturelimit (TH) is derived from the high temperature curing curve and the lowtemperature limit (TL) is derived from the low temperature curing curve.For example, the TH may be the highest temperature on the hightemperature curing curve and the TL may be the lowest temperature on thelow temperature curing curve. Examples of such limits are illustrated inFIG. 3.

Alternatively, in other embodiments, the TH (and by analogy the TL) maybe selected, for example, as an average of the 3 highest (lowest)temperatures on the high (low) temperature curing curve, an average ofall the temperatures on the high (low) temperature curing curve, thethird highest (lowest) temperature on the high (low) temperature curingcurve or any other selection that would be suitable for a givenapplication.

It should be noted that since each of the curing curves has a toleranceover which the cure may take place, (FC in FIG. 5), the acceptabletolerance applies to the TH and the TL that are derived from the highand low temperature curing curves. For example, if the high temperaturelimit is derived from the high temperature curing curve as being 130°C., and the acceptable tolerance is 5° C., then the high temperaturelimit may be derived from the high temperature curing curve as being ashigh as 135° C. Likewise, if the low temperature limit is derived fromthe low temperature curing curve as being 75° C., and the acceptabletolerance is 5° C., then the low temperature limit may be derived fromthe low temperature curing curve as being as low as 70° C.

Advantageously, if the TH and the TL are sufficiently separated, thearticle may have a compliant cure over a much wider temperature rangeduring the curing process, therefore reducing the chances of anon-compliant cure that would be caused should, for example, themeasured cure temperature dip to below the acceptable measured curetemperature. Without limiting the invention, particular embodiments ofthe present invention include a difference between the high temperaturelimit and the low temperature limit of between 10° C. and 50° C.,between 15° C. and 70° C., between 20° C. and 35° C. or between 5° C.and 70° C. Other embodiments include a temperature difference that is atleast 5° C., at least 10° C. or at least 35° C.

Particular embodiments of the present invention for the method of curinga rubber article may further include the step of obtaining a curingtarget A1 or A2, wherein A1 is an area between the high temperaturecuring curve and a base temperature (TB) and A2 is an area between thelow temperature curing curve and the TB, wherein the TB is selected tomake A1 and A2 within at least 10% of each other. Particular embodimentsof the present invention for the method of curing a rubber article mayfurther include the step of obtaining the base temperature.

In particular embodiments, the curing target and base temperature forexample, may be obtained by the controller 20 from a database or from amanual operator input. An operator may enter the curing target or basetemperature at the user interface 28. The data may be stored in thememory device 22 as a value to be obtained by the controller 20.

Typically, the base temperature (TB) is less than the low temperaturelimit (TL). Without limiting the invention, particular embodiments ofthe present invention include a difference between TB and TL that may beas little as 5° C. or 15° C. and as much as 70° C.

Because the measured temperature within the autoclave is allowed to varyanywhere between the TH and the TL, a curing target must be set fordetermining when a compliant cure is achieved. The curing target may beset as being equal to the area under the high temperature curing curveand a base temperature or equal to the area under the low temperaturecuring curve and the base temperature. In particular embodiments of thepresent invention, the base temperature is set to make these two targetareas within at least 10% of each other. In alternate embodiments, thebase temperature is set to make these target areas, for example, withinat least 5% of each other or equal to each other.

FIGS. 6 and 7 are graphs showing the target area between a hightemperature curing curve and the base temperature and the target areabetween a low temperature curing curve and the base temperaturerespectively. As shown in FIGS. 6 and 7, and as expected, the hightemperature curing curve 71 of the example shown cures an article in ashorter period of time (50 min) than the period of time (80 min)required to cure the article according to the low temperature curingcurve 75 of FIG. 7.

In the example provided, the base temperature TB was chosen to make thetarget area 72 between the high temperature curing curve 71 and the TBequal to the target area 76 between the low temperature curing curve 75and the TB.

There are many ways to determine or calculate the TB that makes thetarget areas 72, 76 equal. If, as in the example of FIGS. 6 and 7 thetarget areas 72, 76 are essentially rectangles, the target areas may becalculated as:A1=(CH−TB)(CTH)  (1)A2=(CL−TB)(CTL)  (2)wherein A1 is the target area under the high temperature curing curve,A2 is the target area under the low temperature curing curve, CH and CLare the high and low curing temperatures respectively and CTH and CTLare the high and low curing times respectively. Since the TB is beingselected to make A1=A2, equations (1) and (2) can be set equal to eachother and solved for TB, resulting in the following equation (3):TB=((CL)(CTL)−(CH)(CTH))/(CTL−CTH).  (3)

Solving Equation (3) with the numbers provided in the example of FIGS. 6and 7 provides a TB of 33.3° C. Inserting that number into eitherequation (1) or (2) provides a cure target of 3336 degrees·minutes forthe example shown in these figures.

Particular embodiments of the present invention for the method of curinga rubber article may further include the steps of determining an areaunder a measured curing curve, the area under the measured curing curvebeing between the measured curing curve and the TB, wherein the measuredcuring curve is defined as a plot of the measured curing temperaturesover time. Such embodiments may include an additional step of indicatinga completed cure when the area under the measured curing curve reachesthe curing target. The step of setting the curing target was discussedabove. Such indicator may be provided, for example by sending a messageto the operator interface 28 or controller 20 or by simply starting tocool the autoclave.

For example, FIG. 8 is a graph showing the area between a measuredcuring curve and the base temperature in accordance with particularembodiments of the present invention. The measured curing curve 81 is aplot of the measured temperatures within the autoclave over time, theautoclave being controlled pursuant to the curing curves shown in FIGS.6 and 7. As shown in the example of FIG. 8, the temperature within theautoclave rises quickly to a temperature between the low temperaturelimit TL and the high temperature limit TH. The cure time starts whenthe temperature reaches the TB at time “ts” and continues until time“tx.” At time “tx”, the area 82 shown under the measured curing curve 81is not equal to the target area. Therefore the curing continues until“tf,” when the additional area 83 under the measured curing curve 81makes the total of the areas 82, 83 under the measured curing curve 81equal to the target area. At that point, a compliant cure has beenachieved.

While there are several methods known to one of ordinary skill in theart for determining the area between the measured curing curve and thebase temperature, one equation that may be used is the followingequation (4):

$\begin{matrix}{\sum\limits_{n = 1}^{tf}{\left( {{TM} - {TB}} \right)_{n}\left( {\Delta\; t} \right)_{n}}} & (4)\end{matrix}$wherein TM is the measured cure temperature, TB is the base temperature,Δt is the time increment over which the nth difference is calculated,and n is the number of time increments taken over the range between thestart of the cure and t_(f), the time when the cure is complete.

FIG. 9 is a flowchart of an exemplary method for curing a rubberarticle, executable on the system of FIG. 1 in accordance with thepresent invention. In state 101, the autoclave containing a rubberarticle to be cured is heated to at least the low temperature limit. Instate 103, the temperature within the autoclave is maintained betweenthe high temperature limit and the low temperature limit.

In state 105, the curing target is set for the cure, the curing targetin this embodiment having the units of degrees·minutes. In state 107,the base temperature is defined.

In state 109, the temperature is measured within the autoclave at 1minute intervals and the base temperature is subtracted from each of themeasured temperatures. In state 111, each of these differences is summedin a running sum of the differences. In state 113, the running sum iscompared to the curing target and if the running sum is less than thecuring target, then the method returns to state 109. If the running sumis at least equal to or greater than the curing target, then the methodcontinues to state 115 and the cure is complete.

The terms “comprising,” “including,” and “having,” as used in the claimsand specification herein, shall be considered as indicating an opengroup that may include other elements not specified. The term“consisting essentially of,” as used in the claims and specificationherein, shall be considered as indicating a partially open group thatmay include other elements not specified, so long as those otherelements do not materially alter the basic and novel characteristics ofthe claimed invention. The terms “a,” “an,” and the singular forms ofwords shall be taken to include the plural form of the same words, suchthat the terms mean that one or more of something is provided. The terms“at least one” and “one or more” are used interchangeably. The term“one” or “single” shall be used to indicate that one and only one ofsomething is intended. Similarly, other specific integer values, such as“two,” are used when a specific number of things is intended. The terms“preferably,” “preferred,” “prefer,” “optionally,” “may,” and similarterms are used to indicate that an item, condition or step beingreferred to is an optional (not required) feature of the invention.Ranges that are described as being “between a and b” are inclusive ofthe values for “a” and “b.”

It should be understood from the foregoing description that variousmodifications and changes may be made to the embodiments of the presentinvention without departing from its true spirit. The foregoingdescription is provided for the purpose of illustration only and shouldnot be construed in a limiting sense. Only the language of the followingclaims should limit the scope of this invention.

What is claimed is:
 1. A method for curing a rubber article, the methodcomprising: maintaining a measured curing temperature (TM) within acuring chamber between a high temperature limit (TH) and a lowtemperature limit (TL), wherein the TH is derived from a hightemperature curing curve and the TL is derived from a low temperaturecuring curve; obtaining a curing target A1 or A2, wherein A1 is an areabetween the high temperature curing curve and a base temperature (TB)and A2 is an area between the low temperature curing curve and the TB,wherein the TB is selected to make A1 and A2 within at least 10% of eachother; determining an area under a measured curing curve, the area underthe measured curing curve being between the measured curing curve andthe TB, wherein the measured curing curve is defined as a plot of themeasured curing temperature over time; and indicating a completed cureof the rubber article when the area under the measured curing curvereaches the curing target.
 2. The method of claim 1, wherein the TB isselected to make A1 and A2 within 5% of each other.
 3. The method ofclaim 1, wherein the TB is selected to make A1 and A2 equal.
 4. Themethod of claim 1, wherein the step of determining the area under themeasured curing curve comprises: calculating the area under the measuredcuring curve using the equation$\sum\limits_{n = 1}^{tf}{\left( {{TM} - {TB}} \right)_{n}\left( {\Delta\; t} \right)_{n}}$wherein TM is the measured curing temperature, TB is the basetemperature, Δt is a time increment over which an nth difference iscalculated and n is the number of time increments taken over a rangebetween a start of the cure to t_(f), a time when the cure is complete.5. The method of claim 1, wherein the difference between the TH and theTL is between 10° C. and 50° C.
 6. The method of claim 1, wherein thedifference between the TH and the TL is between 15° C. and 70° C.
 7. Themethod of claim 1, wherein the article is at least a part of a tire. 8.The method of claim 1, wherein the article is a cushion gum between atire tread and a tire carcass.
 9. The method of claim 1, wherein the THis the highest temperature on the high temperature curing curve.
 10. Themethod of claim 1, wherein the TL is the lowest temperature on the lowtemperature curing curve.
 11. The method of claim 1, wherein the methodfurther comprises: obtaining the base temperature.
 12. A non-transitorycomputer-readable medium encoded with computer-executable instructionsfor a controller processor to perform a method of curing a rubberarticle, the encoded, computer-executable instructions comprising:maintaining instructions for maintaining a measured curing temperature(TM) within a curing chamber between a high temperature limit (TH) and alow temperature limit (TL), wherein the TH is derived from a hightemperature curing curve and the TL is derived from a low temperaturecuring curve; obtaining instructions for obtaining a curing target A1 orA2, wherein A1 is an area between the high temperature curing curve anda base temperature (TB) and A2 is an area between the low temperaturecuring curve and the TB, wherein the TB is selected to make A1 and A2within at least 10% of each other; determining instructions fordetermining an area under a measured curing curve, the area under themeasured curing curve being between the measured curing curve and theTB, wherein the measured curing curve is defined as a plot of themeasured curing temperature over time; and indicating instructions forindicating a completed cure of the rubber article when the area underthe measured curing curve reaches the curing target.
 13. The computerprogram product of claim 12, wherein the TB is selected to make A1 andA2 within 5% of each other.
 14. The computer program product of claim12, wherein the TB is selected to make A1 and A2 equal.
 15. Thenon-transitory computer-readable medium of claim 12, wherein theinstructions for determining the area under the measured curing curvecomprises: calculating instructions for calculating the area under themeasured curing curve using the equation$\sum\limits_{n = 1}^{tf}{\left( {{TM} - {TB}} \right)_{n}\left( {\Delta\; t} \right)_{n}}$wherein TM is the measured curing temperature, TB is the basetemperature, Δt is a time increment over which an nth difference iscalculated and n is the number of time increments taken over a rangebetween a start of the cure and t_(f), a time when the cure is complete.16. The non-transitory computer-readable medium of claim 12, wherein thedifference between the TH and the TL is between 10° C. and 50° C. 17.The non-transitory computer-readable medium of claim 12, wherein thedifference between the TH and the TL is between 15° C. and 70° C. 18.The non-transitory computer-readable medium of claim 12, wherein thearticle is at least a part of a tire.
 19. The non-transitorycomputer-readable medium of claim 12, wherein the article is a cushiongum between a tire tread and a tire carcass.
 20. The non-transitorycomputer-readable medium of claim 12, wherein the TH is the highesttemperature on the high temperature curing curve.
 21. The non-transitorycomputer-readable medium of claim 12, wherein the TL is the lowesttemperature on the low temperature curing curve.
 22. The non-transitorycomputer-readable medium of claim 12, further comprising: obtaininginstructions for obtaining the base temperature.
 23. A system for curinga rubber article, the system comprising: an autoclave comprising achamber that is controllably heated for curing the rubber article; atemperature sensor for generating a signal as a function of a curingtemperature in the chamber of the autoclave; and a controller forcontrolling the curing temperature in the autoclave and for indicating acompleted cure of the rubber article, the controller comprising aprocessor and a memory storage device that stores instructionsexecutable by the processor, such executable instructions including theinstructions of claim 12, wherein the processor executes theinstructions of claim 12.